Method for assisting corneal severity identification using unsupervised machine learning

ABSTRACT

A method for assisting corneal severity identification, the method comprising obtaining a corneal configuration data set of a cornea to be examined by a tomography such as an optical coherence tomography; visualizing the corneal configuration data set of the cornea to be examined along with a number of pre-existing corneal configuration data sets of disorder corneas, disorder-suspect corneas and normal corneas obtained by the tomography using t-distributed Stochastic Neighbor Embedding in a two or three dimensional map, and judging corneal severity from the map.

TECHNICAL FIELD

The invention is related to a method for assisting corneal severityidentification using unsupervised machine learning.

BACKGROUND ART

In corneal diseases, keratoconus, bullous keratopathy, walleye,keratoleukoma, keratohelcosis, herpes corneae, corneal chemical burn,corneal thermal burn, degeneratio corneae and the like can be restoredby a corneal transplant. It is difficult to determine need for thetransplantation.

Keratoconus is a noninflamatory ectatic corneal disorder characterizedby progressive thinning resulting in corneal protrusion and decreasedvision (Non-Patent Document 1). Moderate to advanced keratoconus casesare easily diagnosed due to the presence of classic retinoscopic andbiomicroscopic signs. However, detecting subclinical keratoconus ischallenging because initial manifestations of keratoconus may beunclear, requiring a more comprehensive analysis of cornealcharacteristics including topography, elevation, thickness, andbiomechanical properties (Non-Patent Documents 2 and 3). Many methodshave been suggested for identifying keratoconic eyes using cornealtopography information. However, most of the methods rely on subjectiveanalysis of topographical maps which can be biased by the observer(Non-Patent Document 4).

Among objective approaches for keratoconus identification, machinelearning analysis has gained a lot of attension. Smolek and Klyce(Non-Patent Document 5) proposed a neural network for keratoconusscreening based on corneal topography indices. Chastang et al.(Non-Patent Document 6) introduced a binary decision trees method basedon corneal topography indices to identify clinically apparentkeratoconus from normal cornea. A similar approach was used a few yearslater to identify keratoconus from normal corneas using corneal surfacemodeled with a seventh-order Zernike polynomial (Non-Patent Document 7).All these methods used only anterior topography characteristics ofcornea. However, with the advancement of technology, posterior cornealcurvature and pachymetric data were acquired and used to evaluatecorneal characteristics (Non-Patent Document 8). Pinero et al.documented the corneal volume, pachymetry, and correlation of anteriorand posterior corneal shape in subclinical and clinical keratoconus(Non-Patent Document 9). Perez et al. show that corneal instrumentsincluding videokeratography, Orbscan, and Pentacam together with theindices can lead to early keratoconus detection, however, with anincrease in false positive detection (Non-Patent Document 10).

current methods for automatic detection of keratoconus are mainlysupervised, in the sense that labels and diagnoses are required as inputfor subsequent machine learning. We propose an approach that isnon-biased by either clinician or patient. This approach may lead tobetter identification of form fruste keratoconus which can be hard to doclinically in some cases. Moreover, it provides a non-biased method todetermine progression and need for other treatment, such ascross-linking (Non-Patent Document 11). From big data perspective, theproposed approach is objective without the need to pre-label the eyes.Our results suggest that unsupervised machine learning can be applied tocorneal topography, elevation, and pachymetry parameters to generatehighly specific and sensitive models.

Additionally, Patent Document 1 discloses a method for diagnosing akeratoconus cornea in an eye of a patient which comprises the steps of:providing an electronic model of a cornea, wherein the model includes aplurality of elements, and wherein each element in the model is definedby a plurality of parameters, with each parameter being representativeof tissue qualities in the cornea at the corresponding location of theelement in the model; mapping a topography of the anterior surface ofthe cornea “Ta”; fitting the topography “Ta” to the model to obtain aset of parameters for the plurality of elements; and evaluating the setof parameters to diagnose whether the cornea is keratoconus.

Patent Document 2 discloses a method for measuring a cornea of an eyesaid method comprising: measuring a topography of a cornea experiencinga change in intraocular pressure using an ophthalmological analysissystem during a measurement time interval; obtaining a number of imagedata sets of a surface area of the cornea during the measurement timeinterval, wherein, in the measurement time interval, due to said changein the intraocular pressure, a repeated change in the topography of thecornea in the measurement time interval is caused; and determining therepeated change in the topography of the cornea from the number of imagedata sets, wherein, in each case, the change is measured for points (P)of the surface area of the cornea which were measured during thetopography measurement.

Patent Document 3 discloses a method of analyzing corneal topography ofa cornea comprising the steps of: obtaining corneal curvature data;determining plural indexes characterizing topography of the cornea basedon the obtained corneal curvature data; and judging corneal topographyfrom features inherent in predetermined classifications of cornealtopography using the determined indexes and a neural network so as tojudge at least one of normal cornea, myopic refractive surgery,hyperopic refractive surgery, corneal astigmatism, penetratingkeratoplasty, keratoconus, keratoconus suspect, pellucid marginaldegeneration, or other classification of corneal topography.

CITATION LIST Patent Literatures

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SUMMARY OF THE INVENTION Problem to be Resolved by the Invention

The object of the present invention is to provide a method for assistingcorneal severity identification using unsupervised machine learning, ora method for identifying normal, disorder-suspect and disorder eyes byapplying machine learning to a number of corneal tomography data.

Means for Solving the Problem

The invention is directed to a method for assisting corneal severityidentification.

In one embodiment of the present invention, the method comprises:obtaining a corneal configuration data set of a cornea to be examined bya tomography; visualizing the corneal configuration data set of thecornea to be examined along with a number of pre-existing cornealconfiguration data sets of disorder corneas, disorder-suspect corneasand normal corneas obtained by the tomography using t-distributedStochastic Neighbor Embedding in a two or three dimensional map, andjudging corneal severity from the map.

In another embodiment of the present invention, the corneal severity isat least one selected from the group consisting of keratoconus severity,bullous keratopathy severity, walleye severity, keratoleukoma severity,keratohelcosis severity, herpes corneae severity, corneal chemical burnseverity, corneal thermal burn severity, and degeneratio corneaeseverity.

In another embodiment of the present invention, the cornealconfiguration data set includes at least one of a 2D analysis of ACAviewing surface, a 2D analysis of CCT/ACD viewing surface, STAR360°(Scleral spur Tracking for Angle Analysis and Registration 360°),analysis of lens morphology on 2D Result, analysis of lens morphology on3D Result, analysis of corneal morphology and reference points.

In another embodiment of the present invention, the 2D analysis of ACAviewing surface includes at least one of AOD500, AOD750, ARA500, ARA750,TISA500, TISA750, TIA500, and TIA750 (FIG. 6).

AOD500 (Angle Opening Distance 500) is a distance from AOD500-T toAOD500-IF (mm), wherein AOD500-T is a spot on trabecula (on Cornealinner surface) 500 μm away from SS(Scleral Spur), AOD500-IF is anintersection point of a line passing through AOD500-T and being verticalto a line joining SS and ARA-T with an anterior surface of iris, andARA-T is a point on trabecula (on Corneal inner surface) 750 μm awayfrom SS.

AOD750 (Angle Opening Distance 750 is a distance from ARA-T to ARA-IF(mm), wherein ARA-T is a point on trabecula (on Corneal inner surface)750 μm away from SS and ARA-IF is an intersection point of a linepassing through ARA-T and being vertical to a line joining SS and ARA-Twith an anterior surface of iris.

ARA500 (Angle Recess Area 500) is a square measure of a region of anglerecess bounded by a line joining AOD500-T and AOD500-IF (mm²).

ARA750 (Angle Recess Area 750) is a square measure of a region of anglerecess bounded by a line joining ARA-T and ARA-IF (mm²).

TISA500 (Trabecular Iris Space Area 500) is a square measure of a regionof angle recess bounded by a line joining SS and SS-IF and a linejoining AOD500-T and AOD500-IF (mm²), wherein SS-IF is an intersectionpoint of a line passing through SS and being vertical to a line joiningSS and ARA-T with an anterior surface of iris.

TISA750 (Trabecular Iris Space Area 750) is a square measure of a regionof angle recess bounded by a line joining SS and SS-IF and a linejoining ARA-T and ARA-IF (mm²).

TIA500 (Trabecular-Iris Angle 500) is an angle between a line joining ARand AOD500-T and a line joining AR and AOD500-IF)(°, wherein AR is AngleRecess.

TIA750 (Trabecular-Iris Angle 750) is an angle between a line joining ARand ARA-T and a line joining AR and ARA-IF (°).

In another embodiment of the present invention, the 2D analysis ofCCT/ACD viewing surface includes at least one of CCT, ACD Endo., LV,ACW, CCT, ACD[Epi.], ACD[Endo.], Vault, CLR and ATA.

CCT (Central Corneal Thickness) is a corneal thickness in intersectionof a perpendicular bisector of a line segment (ACW) joining scleralspurs (SSs) with cornea (μm).

ACD Endo. (Anterior Chamber Depth Endothelium) is a depth of theanterior chamber from facies posterior corneae to facies anterior lentis(mm).

LV (Lens Vault) is a distance between facies anterior lentis on aperpendicular bisector of a line segment (ACW) joining scleral spurs(SSs) and perpendicular bisection point of ACW (mm).

ACW (Anterior Chamber Width) is a distance between scleral spurs (SSs)(mm).

CCT (Central Corneal Thickness) is a corneal thickness in intersectionof a perpendicular bisector of a line segment joining angle recesses(ARs) with cornea (μm).

ACD[Epi.] (Anterior Chamber Depth [Epithelium]) is a depth of theanterior chamber from facies anterior corneae to facies anterior lentis(mm).

ACD[Endo.] (Anterior Chamber Depth [Endothelium]) is a depth of theanterior chamber from facies posterior corneae to facies anterior lentis(mm).

Vault (Vault) is a distance from facies posterior phakic (IOL) to faciesanterior lentis (μm).

CLR (Crystalline Lens Rise) is a distance between facies anterior lentison a perpendicular bisector of a line segment (ATA) joining anglerecesses (ARs) and perpendicular bisection point of ATA (μm).

ATA (Angle to Angle) is a distance between angle recesses (ARs) (mm).

In another embodiment of the present invention, the STAR360° (Scleralspur Tracking for Angle Analysis and Registration 360°) includes atleast one of AOD250, AOD500, AOD750, ARA250, ARA500, ARA750, TISA250,TIA500, TIA750, CCT, ACD Endo., LV, ACW, AC.Area, IT750, IT2000, I-Curv.and ITC.

AOD250 (Angle Opening Distance 250) is a distance from AOD250-T toAOD250-IF (mm), wherein AOD250-T is a spot on trabecula (on Cornealinner surface) 250 μm away from SS(Scleral Spur), AOD250-IF is anintersection point of a line passing through AOD250-T and being verticalto a line joining SS and ARA-T with an anterior surface of iris, andARA-T is a point on trabecula (on Corneal inner surface) 750 μm awayfrom SS.

AOD500 (Angle Opening Distance 500) is a distance from AOD500-T toAOD500-IF (mm), wherein AOD500-T is a point on trabecula (on Cornealinner surface) 500 μm away from SS and AOD500-IF is an intersectionpoint of a line passing through AOD500-T and being vertical to a linejoining SS and ARA-T with an anterior surface of iris, and ARA-T is apoint on trabecula (on Corneal inner surface) 750 μm away from SS.

AOD750 (Angle Opening Distance 700) is a distance from ARA-T to ARA-IF(mm), wherein ARA-T is a point on trabecula (on Corneal inner surface)750 μm away from SS and ARA-IF is an intersection point of a linepassing through ARA-T and being vertical to a line joining SS and ARA-Twith an anterior surface of iris.

ARA250 (Angle Recess Area 250) is a square measure of a region of anglerecess bounded by a line joining AOD250-T and AOD250-IF (mm2).

ARA500 (Angle Recess Area 500) a square measure of a region of anglerecess bounded by a line joining AOD500-T and AOD500-IF (mm2).

ARA750 (Angle Recess Area 750) a square measure of a region of anglerecess bounded by a line joining ARA-T and ARA-IF (mm2).

TISA250 (Trabecular Iris Space Area 250) is a square measure of a regionof angle recess bounded by a line joining SS and 55-IF and a linejoining AOD250-T and AOD250-IF (mm2), wherein SS-IF is an intersectionpoint of a line passing through SS and being vertical to a line joiningSS and ARA-T with an anterior surface of iris.

TIA500 (Trabecular-Iris Angle 500) is an angle between a line joining ARand AOD500-T and a line joining AR and AOD500-IF (°), wherein AR isAngle Recess.

TIA750 (Trabecular-Iris Angle 750) an angle between a line joining ARand ARA-T and a line joining AR and ARA-IF)(°.

CCT (Central Corneal Thickness) is a corneal thickness in intersectionof a perpendicular bisector of a line segment (ACW) joining scleralspurs (SSs) with cornea (μm).

ACD Endo. (Anterior Chamber Depth Endothelium) is a depth of theanterior chamber from facies posterior corneae to facies anterior lentis(mm).

LV (Lens Vault) is a distance between facies anterior lentis on aperpendicular bisector of a line segment (ACW) joining scleral spurs(SSs) and perpendicular bisection point of ACW (mm).

ACW (Anterior Chamber Width) is a distance between scleral spurs (SSs)(mm).

AC.Area (Anterior Chamber Area) is a square measure of Anterior Chamber(mm2).

IT750 (Iris Thickness 750) is an iris thickness at a position 750 μmaway from SS (mm).

IT2000 (Iris Thickness 2000) an iris thickness at a position 2000 μmaway from SS (mm).

I-Area (Iris Area) is a square measure of iris (mm2).

I-Curv. (Iris Curvatura) is a maximum of a distance from a line joiningiris root (IR) and contact terminal of lens (IRT) to pigment epithelium(back side) of iris (mm).

ITC (Irido-Trabecular Contact) is contact of iris and trabecula.

In another embodiment of the present invention, the analysis of lensmorphology on 2D Result includes at least one of Front R, Thickness,Diameter, Decentration and Tilt.

Front R (Front Radius) is a curvature radius of facies anterior lentison 2D tomographic view (mm).

Back R (Back Radius) is a curvature radius of facies posterior lentis on2D tomographic view (mm).

Thickness (Thickness) is a thickness of lens on 2D tomographic view(mm).

Diameter (Diameter) is an equatorial diameter of lens on 2D tomographicview (mm).

Decentration (Decentration) is an eccentric distance of a lens centralaxis from an axis (Vertex Normal) passing through apex of cornea on 2Dtomographic view (mm).

Tilt (Tilt) is a tilt of lens center axis relative to an axis (VertexNormal) passing through apex of cornea on 2D tomographic view (°).

In another embodiment of the present invention, the analysis of lensmorphology on 3D Result includes at least one of Front R, Front Rs,Front Rf, Back R, Back Rs, Back Rf, Thickness, Diameter, Decentration,and Tilt.

Front R (Front Radius) is a mean of a steeper meridian Rs and a flattermeridian Rf of a curvature radius of facies anterior lentis on 3D (mm).

Front Rs (Front Radius Steep) is an axis angle (°) and a steepermeridian Rs (mm) of a curvature radius of facies anterior lentis on 3D.

Front Rf (Front Radius Flat) is an axis angle (°) and a flatter meridianRf (mm) of a curvature radius of facies anterior lentis on 3D.

Back R (Back Radius) is a mean of a steeper meridian Rs and a flattermeridian Rf of a curvature radius of facies posterior lentis on 3D (mm).

Back Rs (Back Radius Steep) is an axis angle (°) and a steeper meridianRs (mm) of a curvature radius of facies posterior lentis on 3D.

Back Rf (Back Radius Flat) is an axis angle (°) and a flatter meridianRf (mm) of a curvature radius of facies posterior lentis on 3D.

Thickness (Thickness) is a thickness of lens on 3D (mm).

Diameter (Diameter) is an equatorial diameter of lens on 3D (mm).

Decentration (Decentration) is an axis angle (°) and an eccentricdistance (mm) of a lens central axis from an axis (Vertex Normal)passing through apex of cornea on 3D.

Tilt (Tilt) is a tilt of lens center axis relative to an axis (VertexNormal) passing through apex of cornea on 3D (°).

In another embodiment of the present invention, the analysis of cornealmorphology includes at least one of Ks, Kf, CYL, ACCP, ECC, AA, Apex,Thinnest, and ESI.

Ks (Keratometry Steep) is a steeper meridian equivalent to K2 inKeratometer (D or mm).

Kf (Keratometry Flat) is a flatter meridian equivalent to K1 inKeratometer (D or mm).

CYL (Cylinder) is a corneal astigmatism (D).

ACCP (Average Central Corneal Power) is a mean of corneal refractivepower within a 3 mm diameter (D).

ECC (Eccentricity) is a corneal eccentricity.

AA (Analyzed Area) is ratio of a region available to corneal morphologyanalysis (%).

Apex (Apex) is a thickness of corneal center in corneal thickness map(μm).

Thinnest (Thinnest) is a thickness of thinnest portion in cornealthickness map (μm).

ESI (Ectasia Screening Index) is an index for screening keratoconus.

In another embodiment of the present invention, the reference pointsincludes at least one of SS, AR, IR, IRT, and EP.

SS is Scleral Spur, AR is Angle Recess, IR is Iris Root, IRT is IrisRear Tip (contact terminal of lens), and EP is End Point (ITC terminal).

In another embodiment of the present invention, the cornealconfiguration data set includes at least one of DSI, OSI, CSI, SD_P(4mm), CV_P(4 mm), ACP(3 mm), RMS_E(4 mm), SR_E(4 mm), SR_H(4 mm), CSI_T,SD_T(4 mm), and CV_T(4 mm).

As shown in FIG. 8, a φ9 region of a cornea is divided into 8 equalsectors. Differential Sector Index (DSI) is defined as a differencecalculated by subtracting Min_Area_Power [D] from Max_Area_Power [D].Opposite Sector Index (OSI) is defined as a difference calculated bysubtracting Opposite_Area_Power [D] from Max_Area_Power [D], whereinMax_Area_Power [D] is defined as the highest refractive power (axialpower). Min_Area_Power [D] is defined as the lowest refractive power(axial power).

DSI=Max_Area_Power−Min_Area_Power [D]

OSI=Max_Area_Power−Opposite_Area_Power [D]

Opposite_Area_Power [D] is defined a refractive power (axial power) in asector located on opposite side of a sector having the highestrefractive power (axial power).

Center Surround Index (CSI) is defined as a difference calculated bysubtracting OuterP [D] from InnerP [D], wherein InnerP [D] is arefractive power (axial power) in center region (φ0-3 mm) and OuterP [D]is a refractive power (axial power) in a peripheral region (φ3-6 mm) asshown FIG. 9.

CSI=InnerP−OuterP [D]

Standard Deviation of corneal Power (φ4) (SD_P(4 mm)) is defined as astandard deviation of refractive power (axial power) data within a φ4region of cornea calculated by the following formula.

$\begin{matrix}{{{SD\_ P}( {4\mspace{14mu} {mm}} )} = \sqrt{\frac{\sum\limits_{i = 1}^{N}( {P_{i} - \overset{\_}{P}} )^{2}}{N - 1}}} & \lbrack D\rbrack\end{matrix}$

N is number of refractive power (axial power) data, P is refractivepower (axial power) data, and is an average of refractive power (axialpower).

Coefficient of Variation of corneal Power (φ4) (CV_P(4 mm) is defined asa variation coefficient of refractive power (axial power) data within aφ4 region of cornea calculated by the following formula.

${{CV\_ P}( {4\mspace{14mu} {mm}} )} = \frac{1000 \times {SD\_ P}( {4\mspace{14mu} {mm}} )}{\overset{¯}{P}}$

Average Corneal Power (φ3) (ACP(3 mm) is defined as an average ofrefractive power (axial power) data within a φ4 region of corneacalculated by the following formula. P(i) is a measuring point,PatchArea(i) is a square measurement of the measuring point (FIG. 10).

$\begin{matrix}{{AC{P( {3\mspace{14mu} {mm}} )}} = \frac{\sum\limits_{j = 1}^{N}( {PatchAre{a(i)} \times {P(i)}} )}{\sum\limits_{i = 1}^{N}{PatchAre{a(i)}}}} & \lbrack D\rbrack\end{matrix}$

Root Mean Square of corneal Elevation (φ4) (RMS_E(4 mm)) is defined as aroot mean square of Elevation data within a φ4 region of corneacalculated by the following formula.

${{RMS\_ E}( {4\mspace{14mu} {mm}} )} = \sqrt{\frac{\sum\limits_{i = 1}^{N}E_{i}^{2}}{N}}$

N is number of elevation data, and E is elevation data.

Surface Regularity of corneal Elevation (φ4) (SR_E(4 mm)) is defined asa surface regularity index (SRI) based on Elevation data within a φ4region of cornea calculated by the following formula (FIG. 11).

$\begin{matrix}{{f^{\prime\prime\prime}(i)} = \frac{{- {E_{1}(i)}} + {3{E_{2}(i)}} - {3{E_{3}(i)}} + {E_{4}(i)}}{\Delta {Radius}}} & (I) \\{{SR\_ E} = {1000*\sqrt{\frac{\sum\limits_{i = 1}^{N}{f^{\prime\prime\prime 2}(i)}}{N}}}} & ({II}) \\{{f^{''}(i)} = {{{P_{2}(i)} - \frac{{P_{1}(i)} + {P_{3}(i)}}{2}}}} & ({III}) \\{{SRI} = {{\ln ( {1000*{f^{''}(i)}} )} - 3.5}} & ({IV})\end{matrix}$

Surface Regularity of corneal Height (φ4) (SR_H(4 mm)) is defined as aSurface Regularity Index based on Height data within a φ4 region ofcornea calculated by the following formula (FIG. 12).

$\begin{matrix}{{f^{\prime\prime\prime}(i)} = \frac{{- {H_{1}(i)}} + {3{H_{2}(i)}} - {3{H_{3}(i)}} + {H_{4}(i)}}{\Delta {Radius}}} & (I) \\{{SR\_ H} = {100*\sqrt{\frac{\sum\limits_{i = 1}^{N}( {{PatchA}re{a(i)} \times {f^{\prime\prime\prime 2}(i)}} )}{\sum\limits_{i = 1}^{N}{{Patc}hAre{a(i)}}}}}} & ({II})\end{matrix}$

Center Surround Index of Thickness (CSI_T) is defined as a differencebetween an average thickness of center region (φ3) and an averagethickness of peripheral region (φ6) calculated by the following formula(FIG. 13).

CSI_T=InnerT−OuterT [um]

Standard Deviation of Thickness (φ4) (SD_T(4 mm)) is defined as astandard deviation of corneal thickness (Pachymetry) within a φ4 regionof cornea calculated by the following formula.

$\begin{matrix}{{{SD\_ T}( {4\mspace{14mu} {mm}} )} = \sqrt{\frac{\sum\limits_{i = 1}^{N}( {T_{i} - \overset{\_}{T}} )^{2}}{N - 1}}} & \lbrack D\rbrack\end{matrix}$

Coefficient of Variation of Thickness (φ4) (CV_T(4 mm)) is defined as avariation coefficient of corneal thickness (Pachymetry) within a φ4region of cornea calculated by the following formula.

${{CV\_ T}( {4\mspace{14mu} {mm}} )} = \frac{1000 \times {SD\_ T}( {4\mspace{14mu} {mm}} )}{\overset{¯}{T}}$

In another embodiment of the present invention, the tomography is anoptical coherence tomography.

In another embodiment of the present invention, the optical coherencetomography is an anterior eye part optical coherence tomography.

In another embodiment of the present invention, the optical coherencetomography is a swept-source optical coherence tomography.

Advantageous Effects of the Invention

The proposed method identified four clusters; I: a cluster composed ofmostly normal eyes (224 eyes with ESI equal to zero, 23 eyes with ESIbetween five and 29, and nine eyes with ESI greater than 29), II: acluster composed of mostly healthy eyes and eyes with forme frustekeratoconus (1772 eyes with ESI equal to zero, 698 eyes with ESI betweenfive and 29, and 117 eyes with ESI greater than 29), III: a clustercomposed of mostly eyes with mild keratoconus stage (184 eyes with ESIgreater than 29, 74 eyes with ESI between five and 29, and 6 eyes withESI equal to zero), and IV: a cluster composed of eyes with mostlyadvanced keratoconus stage (80 eyes had ESI greater than 29 and 1 eyehad ESI between five and 29). We found that keratoconus status andseverity can be well identified using unsupervised machine learningalgorithms along with linear and non-linear corneal data transformation.The proposed method can better identify and visualize the cornealdisease stages.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 Applying principal component analysis on corneal features. Left:explained variance of the first 40 significant principal components.Right: corneal features in the space of the first six principalcomponents.

FIG. 2 Evolution of corneal parameters in 2-D tSNE space. Zigzag, leftto right, shows the evolution of tSNE over time starting from initialstate which the corneal parameters are simply collapsed onto a 2-D spaceand then grouping eyes with similar corneal characteristics togetherover time.

FIG. 3 Unsupervised machine learning identified four clusters of eyeswith similar corneal characteristics.

FIG. 4 Mapping ESI index on clustering. Left: ESI index corresponding toanterior segment of cornea, Middle: ESI index corresponding to posteriorsegment of cornea, and Right: overall ESI index of Casia instrument.

FIG. 5 Investigating CLUTO, another density-based clustering algorithm.Top left: CLUTO was applied on the tSNE eigen-parameters and visualizedon the tSNE map, Top right: CLUTO was applied on the PCA components andvisualized on the tSNE map, Bottom left: CLUTO was applied on theoriginal data with 420 parameters and visualized on the tSNE map, Bottomright: CLUTO was applied on the original data and visualized using twosignificant principal components.

FIG. 6 A diagram showing a concept of 2D analysis.

FIG. 7 A diagram showing a concept of STAR360° 2D analysis.

FIG. 8 A diagram showing a φ9 region of a cornea divided into 8 equalsectors.

FIG. 9 A diagram showing a concept of CSI.

FIG. 10 A diagram showing a concept of measuring point.

FIG. 11 A diagram showing a concept of Elevation.

FIG. 12 A diagram showing a concept of Height.

FIG. 13 A diagram showing a concept of CSI_T.

EMBODIMENTS FOR CARRYING OUT THE INVENTION

In this multi-center retrospective study, we collected corneal opticalcoherence tomography (OCT) images from 12,242 eyes of 3162 subjectsusing SS-1000 CASIA OCT Imaging Systems (Tomey, Japan) and otherparameters from the electronic health record (EHR) system. All dataavailable at each instrument was collected without any pre-condition. Wethen selected a single visit from each eye and excluded eyes withmissing Ectasia Status Index (ESI). A total of 3,156 eyes met thecriterion. About 57% of the participants were female and the mean agewas 69.7 (standard deviation; SD=16.2) years. Three screening labelswere derived from the ESI index of Casia (produced by TOMEYCorporation); normal if ESI is between 0 and 4, forme fruste keratoconus(or keratoconus-suspect) if ESI is between 5 and 29, and keratoconus ifESI is 30 or greater. Using Casia labels, our dataset included 1970healthy eyes, 796 eyes with forme fruste keratoconus, and 390 eyes withkeratoconus. ESI is basically an instrument-guided screening index whichhas been shown to have a good agreement with Belin-Ambrosio (BA) indexin diagnosing keratoconus (Non-Patent Document 12). This study wasperformed in accordance with the ethical standards in the Declaration ofHelsinki and institutional review board (IRB) was submitted and approvedin the “Jichi Medical University IRB Office. Data use agreement wassigned between centers in Japan and our institute to conduct theanalysis. The data was de-identified in Japan before any furtherprocessing.

Four hundred and twenty parameters including axial, refractive,elevation, and pachymetry of both anterior and posterior surfaces ofcornea were selected for the unsupervised machine learning analysis. AllESI-related parameters were excluded from the dataset. We first applieda principal component analysis (PCA) using prcomp function in the Rpackage to the 420 selected corneal parameters. PCA uses a linear andorthogonal transformation to convert the observations of highlycorrelated corneal parameters into a set of new parameters which arelinearly uncorrelated to each other. In another word, each new principalcomponent parameter is a weighted combination of all initial cornealparameters while the components do not carry correlation anymore. Thistransformation allowed us to linearly reduce the number of dimensions ofthe original dataset. To investigate how many principal components aresignificant compared to a generated null distribution, we generated 100independent artificial datasets such that within each dataset, thevalues along every corneal parameter were randomly permuted (Non-PatentDocument 13). This operation removes the pairwise correlations betweencorneal parameters while keeping the distribution of every parameterunchanged. We then applied PCA to each of these 100 artificial VFdatasets and sorted the combined eigenvalues of different datasets. Weidentified the principal components in our dataset in which theireigenvalues were significantly greater than the top eigenvalues from theartificial datasets (p<0.01, Bonferroni corrected).

We then applied manifold learning using t-distributed stochasticneighbor embedding (tSNE) (see Non-Patent Document 14) to group eyeswith similar corneal characteristic together and to separate eyes withdissimilar characteristics as far away as possible. We used Rtsnefunction in the R package for this purpose. This process maps eyes withsimilar local distance metrics in the tSNE space and nonlinearly reducethe dimension of input data. Moreover, tSNE is well-suited forvisualization and monitoring the progress of the disease by clinicianssince it provides a user-friendly visualization. Moreover, it allowssubjective validation of the follow-up unsupervised clustering becauseone can see how the clusters are distributed and overlapped in 2- or3-dimensional space. More importantly, tSNE generates more distinct andnon-overlapping clusters compared to the best two principal components.

While there are several unsupervised clustering algorithms foridentifying hidden structures in datasets (Non-Patent Documents 15-20),we employed an unsupervised density-based clustering (see Non-PatentDocument 21) in the tSNE space to identify eyes with similar cornealcharacteristics in tSNE space and to group the eyes into non-overlappingclusters objectively. Density-based clustering groups eyes in the tSNEspace that that are closely packed together and have many neighborsaround them while eyes that lie alone (in low-density areas) and are toofar away will be marked as outlies and not members of groups. We thenassessed the accuracy of the approach both qualitatively (visualization)and quantitatively (using screening index of the Casia instrument).

FIG. 1 (left) shows the top 40 principal components and the amount ofvariance in data explained by those components. We identified 32principal components as significant based on our quantitative analysis.The top 32 principal components explained over 80% of the totalvariability in the data while the top eight principal components carriedapproximately 60% of the total variability in the data. However, afterinvestigating tSNE maps, we selected 8 principal components which showeda more discriminative clusters on the tSNE map (qualitative validation).We generated two corneal eigen-parameters which is essentially anonlinear combination of original corneal parameters.

FIG. 2 shows the evolution of tSNE over time starting from the initialstate in which the corneal parameters are collapsed in 2-D space withoutconsidering the local characteristics among points. We selected 2-Dbecause it provides a user-friendly, importantly, a clinician-friendlyvisualization. The algorithm then identifies eyes with similarcharacteristics based on their distances in the tSNE space and graduallygroups them together. The perplexity which reflects the assumed numberfor the neighbors for each point was set to 34 and we allowed themaximum number of iterations to 1000.

To subjectively assess the accuracy of learning, we applied unsuperviseddensity-based clustering on the two identified corneal eigen-parameters.Clusters with fewer than seven eyes were excluded. Unsuperviseddensity-based clustering identified four non-overlapping clusters. For abetter visualization, we color-coded the clusters as shown in FIG. 3.

We then assigned clinical labels to the four identified clusters basedon the ESI index (ranging from 0 to 100) provided by Casia instrument,where zero indicates normal and 100 reflects the most advanced stage ofkeratoconus. Casia instrument also provides diagnostic labels based onthe ESI index: normal if ESI equals to zero, forme fruste keratoconus(or keratoconus-suspect) if ESI is between 5 and 29, and keratoconus ifESI is greater than 29. However, it is unclear how this index isgenerated from all corneal parameters and, more importantly, how thethreshold for identifying eyes with forme fruste keratoconus isidentified. Moreover, the currently used forme fruste keratoconusthreshold index is confusing by its nature since keratoconus representsa spectrum of corneal deformations particularly in the early stages ofthe disease and it is challenging to assign a binary label to segregatea normal eye from an eye with forme fruste keratoconus. Nevertheless,using the Casia ESI index and diagnostic labeling convention, wedetermined that cluster I (color-coded black) was mainly composed ofhealthy eyes: 224 healthy eyes, 23 eyes with forme fruste keratoconus,and nine eyes with keratoconus. Cluster II (color-coded gray—big clusteron the left) was mainly composed of healthy eyes and eyes with formefruste keratoconus: 1772 healthy eyes, 698 eyes with forme frustekeratoconus, and 117 eyes with keratoconus. Cluster III (color-codedlight gray) was mostly composed of eyes with mild keratoconus: 184 eyeswith mild keratoconus, 74 eyes with forme fruste keratoconus, and sixhealthy eyes. The small cluster IV (color-coded white-triangular black)was mainly composed of eyes with advanced keratoconus: 80 eyes withadvanced keratoconus and one eye with forme-fruste keratoconus.

To subjectively evaluate the correlation between the severity ofkeratoconus of eyes in the identified clusters and the ESI index of theCasia instrument, we color-coded each eye on the clustering plot withanterior, posterior, and total ESI indices reflecting the severity ofkeratoconus. FIG. 4 shows the mapping of anterior, posterior, and totalESI indices onto the clusters we identified.

To objectively assess the accuracy of unsupervised clustering, wecomputed the specificity and sensitivity based on Casia diagnosticlabeling. The specificity of identifying healthy eyes from eyes withkeratoconus was 94.1% and the sensitivity of identifying eyes withkeratoconus from healthy eyes was 97.7%.

To compare the DBSCAN clustering algorithm to other approaches, weinvestigated the OPTICS (Non-Patent Document 19] and the ClusteringToolkit (CLUTO) algorithm (Non-Patent Document 20). CLUTO is a softwarepackage for unsupervised clustering of low- and high-dimensionaldatasets. We first applied CLUTO on the tSNE and visualized the outcome.We then asked whether CLUTO generates more discriminant clusters usingprincipal components or the original data with 420 parameters. FIG. 5shows how CLUTO clustered the eyes using tSNE eigen-parameters,principal components, and original data. As can be seen, none of theoutcomes generated a well-separated clusters. To assess the outcome ofclustering objectively, we further investigated the specificity andsensitivity of the clusters using the same approach that we performedfor DBSCAN. We determined that DNCLUE generates four clusters that aretypically normal and one cluster that is abnormal. We used optics andskmeans functions in R to implement OPTICS and CLUTO, respectively.

To investigate the clusters generated by CLUTO algorithm objectively, wecalculated the specificity and sensitivity of CLUTO applied to theoriginal data with 420 parameters. The specificity of identifyinghealthy eyes from eyes with keratoconus was 97.4% and the sensitivity ofidentifying eyes with keratoconus from healthy eyes was 96.3%. However,we selected DBSCAN applied on tSNE since this combination provided anacceptable accuracy and well-separated clusters matched with differentstages of keratoconus.

The major finding of our study is that automated, unsupervisedclustering algorithms using topographic, tomographic, and thicknessprofiles of cornea provides a specific and sensitive means fordetermining keratoconus status and severity. The proposed unsupervisedmachine learning analysis for keratoconus diagnosis and staging providesa promising tool for improving the early detection of initial stages ofkeratoconus and for potential monitoring of treatment for the disease.

Marc Amsler first described how keratoconus manifests in altered cornealtopography in 1938; however, the introduction of computer-aidedvideokeratoscopy in the early 1980's revolutionized the diagnosis ofkeratoconus. Most of the early methods and severity indexes foridentifying keratoconus have subsequently been based on cornealtopography (see Non-Patent Documents 2, 4, 9, and 22-25). More recentlyit was determined that pachymetric indices were better able todifferentiate healthy eyes from eyes with keratoconus, based on a cohortof 44 eyes with keratoconus and 113 healthy eyes (Non-Patent Document26). However, in the current study we used topography, elevation, andthickness profiles of corneal extracted from optical coherencetomography (OCT) images from subjects using the SS-1000 Casia toidentify and stage keratoconus.

Historically, classification of the stages of keratoconus has been basedon qualitative analysis of overall corneal morphology. However, we usedmachine learning because it addresses limitations of currently useddiagnosis methods, including qualitative rather than quantitativeparameter assessments and observer bias. While machine learningalgorithms for keratoconus have been previously proposed, most are basedon either a single type of corneal parameter (e.g., topography alone)(Non-Patent Documents 23-25) or require pre-labeled data (Non-PatentDocuments 4, 7 and 27). For instance, some researchers have usedsupervised neural network or tree-based classification to discriminatebetween normal eyes and eyes with keratoconus (Non-Patent Documents 4and 27-29). However, pre-labeling an eye as keratoconus or forme frustekeratoconus subjectively itself is prone to subjective evaluation andbias.

We used approximately 420 corneal parameters generated by Casiainstrument through swept source OCT images of the cornea. All thesecorneal parameters were transformed to a 2-D space using linear PCA andnon-linear tSNE followed by an unsupervised machine learning algorithm.Therefore, we first extract the information that is highly predictableof the corneal status instead of feeding all parameters to the machinelearning and confuse its prediction. However, most of the machinelearning algorithms in the literature simply input different cornealparameters to a machine learning algorithm to identify keratoconuswithout leveraging the power of data transformation and extracting mostinformative knowledge for identifying disease.

To investigate whether PCA alone is able to generate well-separatedclusters comparable to those identified by the combination of the PCAand tSNE, we applied PCA alone and performed clustering. We found thatPCA alone generated clusters with significant overlap. We also appliedCLUTO on the selected principal component to compare the outcome withtSNE and observed similar overlapping clusters (FIG. 5, top right).

Subjective assessment of the quality of learning using visualization ofthe clusters and overlaying the ESI keratoconus index of the Casia (asshown in FIG. 4) revealed that the ESI index of anterior corneal surfaceis highly correlated to the keratoconus severity of the eyes weidentified in clusters. Specifically, the eyes in the Cluster IV (colorcoded white-triangular black) and classified as having advancedkeratoconus by machine learning, have high agreement with anterior,posterior, and overall ESI indices since almost all eyes in this clusterhave black.

The same analogy holds for eyes in Cluster I (color coded black)classified as normal, based on machine learning. However, for ClusterIII (small cluster, color coded light gray), which represents mildkeratoconus based on machine learning, eyes generally have a worseposterior ESI index compared to their anterior ESI index (FIG. 4, leftand middle panels). This finding may suggest that posterior cornealparameters better identify keratoconus; however, this finding needsfurther investigation. We also hypothesize that eyes, labeled as normalby Casia ESI labeling system, falling in this cluster are likely “formefruste” keratoconus candidates which need more attention fromclinicians. Finally, Cluster II (color coded dark gray) that representshealthy eyes and eyes suspect of keratoconus based on machine learning,is in strong agreement with all ESI indices except at the far righttail. The eyes in this region are not in a good agreement with anteriorand overall ESI indices. We hypothesize that this region could be aeither a separate cluster or part of cluster III that we were unable toidentify based on current data and algorithms used. It is also possiblethat the eyes in this small region have other eye conditions along withmild keratoconus for which we did not have enough information tocharacterize. However, FIG. 4 (middle panel) indicates that theposterior ESI index was more effective than anterior ESI index (FIG. 4,left panel). In fact, a study conducted by the Ambrosio group shows thatposterior features are superior to anterior features in identifyingkeratoconus (Non-Patent Document 30).

To objectively assess the clinical labels we assigned to clusters withthe severity of eyes in those clusters, we assessed the number of eyeswith either large or small ESI. All eyes in Cluster IV (advancedkeratoconus by machine learning) had ESI index greater than 38. In thisgroup 71 (out of 81) eyes had ESI greater than 60, which indicatesadvanced stages of keratoconus. For Cluster I (normal by machinelearning), only seven eyes (out of 256) had an ESI index greater than30, indicating that the overwhelming majority of eyes in this clusterwere normal. Therefore, our clustering is in good agreement with ESI atthe two sides of spectrum. Based on Casia ESI diagnosis labels, thespecificity of our machine learning method in identifying normal fromkeratoconus eyes was 94.1% and the sensitivity of identifyingkeratoconus from normal eyes was 97.7%, considering only normal andadvanced keratoconus clusters.

There are a number of limitations to our study which could be addressedin follow-up studies. We compared the clustering outcome with Casia ESIindex and showed that there is a good agreement between our finding andESI index spectrum (FIGS. 3 and 4). However, to assess thegeneralizability of this unsupervised clustering approach method, itneeds to be validated by other keratoconus indices such asBellin-Ambrosio (BA) index. Therefore, it is required to conduct anotherstudy to confirm how this approach is generalizable to cornealparameters generated by Pentacam instrument by accessing such datasets.Also, the accuracy of this approach can be validated if the clinicaldiagnosis labels of all eyes were available. However, accessing clinicaldiagnosis labels for all eyes in such big datasets is a challenging andtedious task. Nevertheless, it is beneficial to assess the proposedapproach in a follow-up study with a dataset that includes clinicaldiagnosis labels.

We performed a qualitative and quantitate assessment to determinewhether PCA alone or other clustering approaches generate well-separatedclusters. We found that the OPTICS density-based clustering approach wasable to segregate eyes at different stages of keratoconus while theCLUTO unsupervised clustering approach generated overlapping clusters.However, the most important aspect of our proposed approach lies in thevisualization property and the tSNE 2-D map. This is critical inpractical clinical settings in which it is more appropriate to monitorthe progression of the diseases on a 2-D map rather than proposing ablack-box without 2-D visualization.

In summary, we proposed a possible solution to address shortcomings ofcurrent approaches in keratoconus diagnosis and monitoring, includingobserver bias in pre-defining diagnosis and limitations in the providingonly a binary outcome that the eye belongs to either normal or diseasegroup. The introduced unsupervised machine learning algorithm requiresno pre-labeled data for training and can automatically identify thekeratoconus status of a given eye based on comprehensive cornealparameters, including topography, elevation, and thickness profiles.More importantly, it provides visualization of the status of the eyecompared to other eyes at different stages of keratoconus which was lackin supervised machine learning methods. To the best of our knowledge,this is the first attempt to develop a fully unsupervised algorithm forkeratoconus identification and monitoring.

Keratoconus status and severity can now be well identified usingautomated unsupervised clustering algorithms using topographic,tomographic, and thickness profiles of cornea. This approach can be usedin corneal clinics and research settings to better diagnose, monitorchanges and progression and improve our understanding of corneal changesin keratoconus.

It should be understood that the present invention can be used in manydifferent ways and for many different applications to dramaticallyimprove the corneal severity identification.

1. A method for assisting corneal severity identification, the methodcomprising: obtaining a corneal configuration data set of a cornea to beexamined by a tomography; visualizing the corneal configuration data setof the cornea to be examined along with a number of pre-existing cornealconfiguration data sets of disorder corneas, disorder-suspect corneasand normal corneas obtained by the tomography using t-distributedStochastic Neighbor Embedding in a two or three dimensional map, andjudging corneal severity from the map.
 2. The method according to claim1, wherein the corneal severity is at least one selected from the groupconsisting of keratoconus severity, bullous keratopathy severity,walleye severity, keratoleukoma severity, keratohelcosis severity,herpes corneae severity, corneal chemical burn severity, corneal thermalburn severity, and degeneratio corneae severity.
 3. The method accordingto claim 1, wherein the corneal configuration data set comprises atleast one of a 2D analysis of ACA viewing surface, a 2D analysis ofCCT/ACD viewing surface, STAR360°, analysis of lens morphology on 2DResult, analysis of lens morphology on 3D Result, analysis of cornealmorphology and reference point.
 4. The method according to claim 3,wherein the 2D analysis of ACA viewing surface comprises at least one ofAOD500, AOD750, ARA500, ARA750, TISA500, TISA750, TIA500, and TIA750. 5.The method according to claim 3, wherein the 2D analysis of CCT/ACDviewing surface comprises at least one of CCT, ACD Endo., LV, ACW, CCT,ACD[Epi.], ACD[Endo.], Vault, CLR and ATA.
 6. The method according toclaim 3, wherein the STAR360° comprises at least one of AOD250, AOD500,AOD750, ARA250, ARA500, ARA750, TISA250, TIA500, TIA750, CCT, ACD Endo.,LV, ACW, AC.Area, IT750, IT2000, I-Curv. and ITC.
 7. The methodaccording to claim 3, wherein the analysis of lens morphology on 2DResult comprises at least one of Front R, Thickness, Diameter,Decentration and Tilt.
 8. The method according to claim 3, wherein theanalysis of lens morphology on 3D Result comprises at least one of FrontR, Front Rs, Front Rf, Back R, Back Rs, Back Rf, Thickness, Diameter,Decentration, and Tilt.
 9. The method according to claim 3, wherein theanalysis of corneal morphology comprises at least one of Ks, Kf, CYL,ACCP, ECC, AA, Apex, Thinnest, and ESI.
 10. The method according toclaim 3, wherein the reference point comprises at least one of SS, AR,IR, IRT, and EP.
 11. The method according to claim 1, wherein thecorneal configuration data set comprises at least one of DSI, OSI, CSI,SD_P(4 mm), CV_P(4 mm), ACP(3 mm), RMS_E(4 mm), SR_E(4 mm), SR_H(4 mm),CSI_T, SD_T(4 mm), and CV_T(4 mm).
 12. The method according to claim 1,wherein the tomography is an optical coherence tomography.
 13. Themethod according to claim 1, wherein the optical coherence tomography isan anterior eye part optical coherence tomography.
 14. The methodaccording to claim 1, wherein the optical coherence tomography is aswept-source optical coherence tomography.